Design of observers for switched discrete-time linear systems

An approach to estimation based on Luenberger-like observers is considered for a class of switched discrete-time linear systems. Three observers are proposed. The first one is based only on the satisfaction of stability conditions for the error dynamics, which can be expressed by means of linear matrix inequalities (LMIs). The second observer is basically the first one but its design is accomplished by minimizing an upper bound on a quadratic cost function of the estimation error using LMI-based optimization techniques. The third observer differs from the previous ones as it is constructed by using a projection technique. Simulation results are reported to show the effectiveness of the proposed estimation methods.